Abstract
We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold sigma , we associate an integer-valued function, called degree, measuring the extent to which sigma fails to be cylindrical. In particular, we show that if the degree is constant and equal to d, then the singularities of sigma can only occur along an (m-d)-dimensional “striction” submanifold. This result allows us to extend the standard classification of developable surfaces in {mathbb {R}}^{3} to the whole family of flat and ruled submanifolds without planar points, also known as rank-one: an open and dense subset of every rank-one submanifold is the union of cylindrical, conical, and tangent regions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
